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Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities. (English) Zbl 1191.86030
Summary: Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales.
Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts.
Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere.
Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

##### MSC:
 86A60 Geological problems 80A20 Heat and mass transfer, heat flow (MSC2010)
##### Keywords:
boundary layers; heat transfer; numerical analysis
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##### References:
 [1] DOI: 10.1017/S0022112086002628 · Zbl 0587.76165 · doi:10.1017/S0022112086002628 [2] DOI: 10.1029/JB091iB02p01961 · doi:10.1029/JB091iB02p01961 [3] DOI: 10.1016/S0985-3111(98)80006-5 · doi:10.1016/S0985-3111(98)80006-5 [4] DOI: 10.1016/S0040-1951(00)00084-6 · doi:10.1016/S0040-1951(00)00084-6 [5] DOI: 10.1029/96JB03271 · doi:10.1029/96JB03271 [6] DOI: 10.1093/petrology/25.3.713 · doi:10.1093/petrology/25.3.713 [7] DOI: 10.1144/gsjgs.144.2.0299 · doi:10.1144/gsjgs.144.2.0299 [8] DOI: 10.2475/ajs.295.5.581 · doi:10.2475/ajs.295.5.581 [9] DOI: 10.2475/ajs.295.6.639 · doi:10.2475/ajs.295.6.639 [10] DOI: 10.1029/JB078i035p08735 · doi:10.1029/JB078i035p08735 [11] DOI: 10.1086/628908 · doi:10.1086/628908 [12] DOI: 10.1029/WR025i001p00093 · doi:10.1029/WR025i001p00093 [13] DOI: 10.1016/0045-7825(95)00891-8 · Zbl 0865.76088 · doi:10.1016/0045-7825(95)00891-8 [14] DOI: 10.1016/S0045-7825(98)00038-3 · Zbl 0954.74076 · doi:10.1016/S0045-7825(98)00038-3 [15] DOI: 10.1016/S0045-7825(99)80003-6 · Zbl 0960.76092 · doi:10.1016/S0045-7825(99)80003-6 [16] DOI: 10.1002/(SICI)1096-9853(199712)21:12<863::AID-NAG923>3.0.CO;2-F · doi:10.1002/(SICI)1096-9853(199712)21:12<863::AID-NAG923>3.0.CO;2-F [17] DOI: 10.1108/02644400010334801 · Zbl 1112.76429 · doi:10.1108/02644400010334801 [18] DOI: 10.1002/1099-0887(200102)17:2<101::AID-CNM391>3.0.CO;2-P · Zbl 0986.76049 · doi:10.1002/1099-0887(200102)17:2<101::AID-CNM391>3.0.CO;2-P [19] DOI: 10.1046/j.1365-246X.2003.02032.x · doi:10.1046/j.1365-246X.2003.02032.x [20] DOI: 10.1108/02644400210423990 · Zbl 1012.76527 · doi:10.1108/02644400210423990
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